In this paper, we generalize previous studies on right ideals of prime ring 𝑅 with generalized 𝛼 - derivation 𝐷 and show that 𝑅 is commutative under different conditions. Also, we investigate commutative property of prime ring 𝑅 for two generalized 𝛼 - derivations 𝐷 and 𝐻. [ABSTRACT FROM AUTHOR]